Why are the solutions to 4sin(x)cos(x)=1

(π/12),(5π/12),(13π/12) and (17π/12)? I understand the (π/12), but there are unsymmetrical gaps in between the answers to the equation.

Question

Why are the solutions to 4sin(x)cos(x)=1

(π/12),(5π/12),(13π/12) and (17π/12)?  I understand the (π/12), but there are unsymmetrical gaps in between the answers to the equation.

loser66 · Answer

show me how you get those answer, please

anonymous · Answer

I got (π/12) myself, the rest are from the answers from the back of the book.  (There's no point in writing them down if you don't know how you got them.)

anonymous · Answer

4sin(x)cos(x)=1  

2sin(2x)=1
*(1/2)      *(1/2) 

sin(2x)=(1/2)            sinx(1/2) at (π/6)   (π/6)/(1/2) = (π/12)

anonymous · Answer

maybe I did that wrong, I don't really know

loser66 · Answer

you are very good at this. ok. now I set 2x = $\theta$ got me?

anonymous · Answer

*sinx=(1/2) at (π/6)

anonymous · Answer

I am aware of adding 90 degrees (or something) to get every answer from 0 to 2π, but the answer don't follow that.

loser66 · Answer

so, for 1/2 you have 2 values of $\theta$ not just 1. I show you about $\huge \theta$
 $sin\theta = \dfrac{1}{2}$ $\rightarrow \theta =\dfrac{\pi}{6}~~and~~ \theta = \dfrac{5\pi}{6}$|dw:1384653863060:dw|